Students in a class are arranged to form groups of 4

[M7MBA]

Students in a class are arranged to form groups of 4 members each. After forming the groups, 3 students are left. If the students had been arranged in groups of 9 members each, however, 4 students would be left. What is the total number of students in the class?

(1) The number of students is a two-digit number less than 70.
(2) The number of students is a two-digit number greater than 50.

The OA is B.

Should I find a number that when divided by 4 the remainder is 3 and when divided by 9 the remainder is 4? How can I solve it? Thanks in advanced.

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Hi M7MBA,

We're told that the students in a class are arranged to form groups of 4 members each and after forming the groups, 3 students are left. If the students had been arranged in groups of 9 members each, however, 4 students would be left. We're asked for the total number of students in the class. This question can be answered by TESTing VALUES and a bit of 'brute force' arithmetic.

To start, we can use the information we're given to list out some of the possibilities (the Facts mention 2-digit numbers, so we'll stick to just those):
-When we form groups of 4 members each, there 3 students are left. The total COULD be 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71, 75, 79, 83, 87, 91, 95, 99
-When we form groups of 9 members each, there 4 students are left. The total COULD be 13, 22, 31, 40, 49, 58, 67, 76, 85, 94
There are only 2 possibilities that are just 2-digits: 31 and 67

1) The number of students is a two-digit number less than 70.

With the information in Fact 1, we know that the total could be 31 or 67.
Fact 1 is INSUFFICIENT

2) The number of students is a two-digit number greater than 50.

With the information in Fact 2, we know that the total could only be 67.
Fact 2 is SUFFICIENT

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

[Scott@TargetTestPrep]

Students in a class are arranged to form groups of 4 members each. After forming the groups, 3 students are left. If the students had been arranged in groups of 9 members each, however, 4 students would be left. What is the total number of students in the class?

(1) The number of students is a two-digit number less than 70.
(2) The number of students is a two-digit number greater than 50.

We are given that when we divide the total students by 4, we have a remainder of 3, so the total could be values such as:

7, 11, 15, 19, 23, 27, 31, 35, 39, ...

We are given that when we divide the total students by 9, we have a remainder of 4, so the total could be values such as:

13, 22, 31, 40, 49, 58, ...

The first value common to our lists is 31; we can keep adding the LCM of 4 and 9, which is 36, to 31 to generate succeeding values. Thus, the total number of students could be:

31, 67, 103, ...


We need to determine the exact total number of students.

Statement One Alone:

The number of students is a two-digit number less than 70.

Since the total number of students could be 31 or 67, statement one alone is not sufficient to answer the question.

Statement Two Alone:

The number of students is a two-digit number greater than 50.

Of the numbers 31, 67, 103, ... there is only one number that is both a 2-digit number and greater than 50. Thus, statement two is sufficient.

Answer: B